E-Dissertationen: Browsing E-Dissertationen by Author "Zagier, Don Bernard"
Now showing items 1-9 of 9
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Analytische und p−adische Aspekte von klassischen und Mock-Modulformen
Fricke, Karl-Heinz (2013-10-17)Ausgangsfrage dieser Doktorarbeit war die Gleichverteilung von geschlossenen Geodaetischen im Fundamentalbereich der Modulgruppe in der hyperbolischen Geometrie. Das fuehrt auf das Studium der Eigenfunktionen des ... -
Dual weights in the theory of harmonic Siegel modular forms
Raum, Martin (2012-07-13)We define harmonic Siegel modular forms based on a completely new approach using vector-valued covariant operators. The Fourier expansions of such forms are investigated for two distinct slash actions. Two very different ... -
Elliptic multiple zeta values, modular graph functions and genus 1 superstring scattering amplitudes
Zerbini, Federico (2018-03-05)We study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are ... -
Factorization of holomorphic eta quotients
Bhattacharya, Soumya (2014-12-12)We conjecture the occurrence of a certain type of factor of a holomorphic eta quotient whenever it is reducible and we prove this conjecture for all prime power levels. In particular, this also implies that rescaling and ... -
Higher cross-ratios and geometric functional equations for polylogarithms
Radchenko, Danylo (2016-08-31)In this work we define and study a generalization of the classical cross-ratio. Roughly speaking, a generalized cross-ratio is a function of n points in a projective space that is invariant under the change of coordinates ... -
Higher Green’s functions for modular forms
Mellit, Anton (2009-03-12)Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of ... -
Modular Functions and Special Cycles
Viazovska, Maryna (2013-11-27)In this thesis we study algebraic cycles on Shimura varieties of orthogonal type. Such varieties are a higher dimensional generalization of modular curves and their important feature is that they have natural families of ... -
On discrete surfaces: Enumerative geometry, matrix models and universality classes via topological recursion
Garcia-Failde, Elba (2019-03-21)The main objects under consideration in this thesis are called maps, a certain class of graphs embedded on surfaces. We approach our study of these objects from different perspectives, namely bijective combinatorics, matrix ... -
The Zinger deformation of differential equations with maximal unipotent monodromy
Monsef Shokri, Khosro (2011-10-28)In this thesis, in the first part we study the Zinger deformation for the holomorphic solution of a differential equation with maximal unipotent monodromy. It is basically a generalization of the example made by Zinger, ...